"I think it would be a great advancement," the California Democrat said at her weekly news conference. "Everybody has to make an accommodation."

A coalition of influential LGBT rights organizations jointly pulled endorsements earlier this week of the legislation, partly in protest of the recent Supreme Court Hobby Lobby decision. The Senate bill's "conscience clause," they said, is now too bitter a pill to swallow.

The American Civil Liberties Union, the Gay & Lesbian Advocates and Defenders, Lambda Legal, the National Center for Lesbian Rights and the Transgender Law Center wrote:

"The provision in the current version of the Employment Non-Discrimination Act (ENDA) that allows religious organizations to discriminate based on sexual orientation and gender identity has long been a source of significant concern to us. Given the types of workplace discrimination we see increasingly against LGBT people, together with the calls for greater permission to discriminate on religious grounds that followed immediately upon the Supreme Court’s decision last week in Burwell v. Hobby Lobby, it has become clear that the inclusion of this provision is no longer tenable. It would prevent ENDA from providing protections that LGBT people desperately need and would make very bad law with potential further negative effects."